Phase structure of the Kerr-AdS black hole

We study the critical phenomena of Kerr-AdS black hole. Phase structures are observed at different temperatures, ${T}_{L}$, ${T}_{c1}$ and ${T}_{c2}$ with various features. We discuss the thermal stability considering the isothermal compressibility and how phase transitions related to each other. The asymptotic value of the angular momentum also has an implication on separating stable and unstable part. Near critical temperature ${T}_{c1}$, the order parameter is determined to calculate the critical exponents. All the critical exponents $(\ensuremath{\alpha},\ensuremath{\beta},\ensuremath{\gamma},\ensuremath{\delta})=(0,\frac{1}{2},1,3)$ are identical to that of mean field systems. We plot the phase diagram near this critical point, and discuss the scaling symmetry of the free energy.